OS-V: 0531 Laminated Shell Strength Analysis Mechanical Load 1

This problem analyzes the strength of laminated composite shells when subjected to a uniform longitudinal load per unit length.

The model and boundary conditions are described by Hopkins (2005). The resulting ply failure indices are compared against analytical solutions from classical lamination theory (CLT). The results indicate good agreement between OptiStruct and CLT.

Benchmark Model



図 1. Composite Laminate Shell Subjected to Uniform Tensile Load. arrowheads represent applied load

800 mesh elements of CQUAD4 element type were used in this study. The model is fixed at the point A using a SPC card and a uniform longitudinal load per unit length (Nx) of 1500 N/m is applied along edges A-D and B-C using FORCE card.

The material properties are:
Property
Value
Longitudinal Young’s Modulus, El (GPa)
207.0
Transverse Young’s Modulus, Et (GPa)
7.6
Longitudinal Shear Modulus, Glt (GPa)
5.0
Major Poisson’s ratio, υ 12
0.3
Longitudinal Tensile Strength, σ lt (MPa)
500.0
Longitudinal Compressive Strength, σ lc (MPa)
350.0
Transverse Tensile Strength, σ tt (MPa)
5.0
Transverse Compressive Strength, σ tc (MPa)
75.0
In-plane shear strength, τ lt (MPa)
35.0
表 1. Laminate Properties of the Composite Model
Ply Orientation (°) Thickness ( μ m)
1 90.0 0.05
2 -45.0 0.05
3 45.0 0.05
4 0.0 0.05
The geometry of the composite laminate:
Dimension
Value
Length (m)
0.2
Breadth (m)
0.1

Results

表 2 compares the midplane strains computed from OptiStruct (OS) with classical lamination theory (CLT). The midplane strains from CLT presented in 表 2 are of the homogenized composite; therefore, STRAIN I/O should be used. CSTRAIN I/O gives the midplane strains of individual plies. The identical results show that OptiStruct calculates the midplane strains accurately.
表 2. Comparison of Midplane Strains between OptiStruct (OS) and Classical Lamination Theory (CLT)
Midplane Strains Theory OptiStruct Result
ε x 3.176 x 10-4 3.176 x 10-4
ε y -1.447 x 10-4 -1.447 x 10-4
ε xy 1.108 x 10-4 1.108 x 10-4
表 3 and 表 4 illustrate the failure indices (FI) and reserve factor (RF) calculated from OptiStruct and CLT. The FI show a good agreement between the finite element results and analytical solution with a maximum difference of 0.2% in ply 3, -0.05% in ply 3 and 0.20% in ply 3 when Tsai-Wu, Hill and Hoffman failure criteria are used respectively. This verification of numerical results for the criteria is addressed and does not address the merits of a particular criteria.
表 3. Comparison of Failure Index between OptiStruct and CLT
Failure Criteria Ply 1 Ply 2 Ply 3 Ply 4
  Theory OptiStruct Result Theory OptiStruct Result Theory OptiStruct Result Theory OptiStruct Result
Tsai-Wu 0.88402 0.8841 0.37308 0.3731 0.01990 0.01991 -0.34309 -0.343
Hill 0.77952 0.77960 0.16323 0.16330 0.00435 0.00435 0.00136 0.00136
Hoffman 0.88110 0.88140 0.37630 0.37610 0.02004 0.02000 -0.34534 -0.34510
表 4. Comparison of Reserve Factor for each Ply between OptiStruct and CLT
Reserve Factor Ply 1 Ply 2 Ply 3 Ply 4
  Theory OptiStruct Result Theory OptiStruct Result Theory OptiStruct Result Theory OptiStruct Result
Tsai-Wu 1.1223 1.122 2.53671 2.537 14.304 14.3 31.879 31.89
Hill 1.1325 1.133 2.4748 2.475 15.157 15.16 27.124 27.12
Hoffman 1.1259 1.126 2.4944 2.494 14.101 14.1 37.869 37.88

Model Files

必要なモデルファイルのダウンロードについては、モデルファイルへのアクセスを参照してください。

The model files used in this problem include:
  • lssam1_tsai.fem
  • lssam1_hill.fem
  • lssam1_hoff.fem

Reference

NAFEMS R0092 - Benchmarks for membrane and bending analysis of laminated shells. Part 1, Stiffness matrix and thermal characteristics

NAFEMS R0093 - Benchmarks for membrane and bending analysis of laminated shells. Part 2, Strength analysis